Assignment 3

ASSIGNMENT 3

Objective

To compare the results with base simulation and improved shell element properties.

1. Using the crash beam file from the previous assignment, change the run time to 55 ms.
2. Change the number of animation steps during simulation to a minimum of 25 and maximum of 60.
3. Run the base simulation without any modification to element properties.
4. At the end of the simulation, do the energy error and mass error checks and determine whether results would be acceptable.
5. If acceptable, Plot rigid wall forces, internal energy, hourglass energy, contact energy, total energy of the simulations.
6. Change all the shell elements properties to recommended properties, save this as separate, rad files and run the simulation.
7. Compare the results with base simulation and improved shell element properties.

Case 1

Setup and procedure

1. Import the given model.
2. Change the card ENG_ANIM_DT with Tstart as 25.
3. Change the card ENG_RUN with Tstop as 55.
4. Click the analysis from the menu page and press radioss to carry out the analysis.
5. Check the energy error (%) and mass addition at the end of the computation.
6. Load the time history file in hypergraph 2D to plot the results (rigid wall forces, internal energy, hourglass energy, contact energy, total energy of the simulations).

Case 2

Setup and procedure

1. Import the given model.
2. Change the card ENG_ANIM_DT with Tstart as 25.
3. Change the card ENG_RUN with Tstop as 55.
4. Change the properties for hat-section and close-out panel with recommended properties.
5. Click the analysis from the menu page and press radioss to carry out the analysis.
6. Check the energy error (%) and mass addition at the end of the computation.
7. Load the time history file in hypergraph 2D to plot the results (rigid wall forces, internal energy, hourglass energy, contact energy, total energy of the simulations).

Comparison with base simulation and improved shell properties simulation

Case 1: Base simulation Case 2: Improved shell properties simulation

Element error(%) check

Result and conclusion

1. Base simulation is done with Q4 element (Belytsho & Tsay), representing under integrated 4 node element. Whereas, case 2 simulation is done with QEPH element.

2. QEPH has a physical hourglass stabilization at the material level, whereas the Q4 element introduces artificial hourglass energy.

3. In case 1 of under integrated elements (Belytschko shells, solids with 1 integration point), the Hourglass energy can also explain a negative Energy Error since it is not counted in the energy balance. The normal amount of Hourglass energy is about -10% to -15%. Hence, the results are acceptable.

4. In the case of using QEPH shell formulation (I_shell=24) or fully integrated elements, the Energy Error can be slightly positive since there is no Hourglass energy and the computation is much more accurate. An error of +1% or +2% is acceptable. In our work, the obtained error is -0.1% which is within an acceptable limit.

Details of hourglass energy and modes

Hourglass modes are nonphysical modes of deformation that occur under integrated elements and produce no stress. The reduced integration can lead to non-physical zero-energy modes, called hourglass modes.

If the element undergoes deformation without energy being absorbed, then the system is in an unstable state. This phenomenon is known to be an hourglass.

Two methods used to control the formation of hourglassing:

• Perturbation (Q4 elemnts) (Viscous method)
• Physical stabilization (QEPH elements)

https://drive.google.com/drive/folders/1Mt25ti9jdo6jmWpPPAyrBhqvdj09gqhZ?usp=sharing